Edge-ratio network clustering by Variable Neighborhood Search

  • Sonia Cafieri
  • Pierre Hansen
  • Nenad Mladenović
Regular Article


The analysis of networks and in particular the identification of communities, or clusters, is a topic of active research with applications arising in many domains. Several models were proposed for this problem. In reference [S. Cafieri, P. Hansen, L. Liberti, Phys. Rev. E 81, 026105 (2010)], a criterion is proposed for a graph bipartition to be optimal: one seeks to maximize the minimum for both classes of the bipartition of the ratio of inner edges to cut edges (edge-ratio), and it is used in a hierarchical divisive algorithm for community identification in networks. In this paper, we develop a VNS-based heuristic for hierarchical divisive edge-ratio network clustering. A k-neighborhood is defined as move of k entities, i.e., k entities change their membership from one to another cluster. A local search is based on 1-changes and k-changes are used for shaking the incumbent solution. Computational results on datasets from the literature validate the proposed approach.


Statistical and Nonlinear Physics 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sonia Cafieri
    • 1
    • 2
  • Pierre Hansen
    • 3
  • Nenad Mladenović
    • 4
  1. 1.ENAC, MAIAAToulouseFrance
  2. 2.IMTUniversity of ToulouseToulouseFrance
  3. 3.GERAD, HEC MontréalMontréalCanada
  4. 4.LAMIHUniversity of ValenciennesValenciennesFrance

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